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Technical Appendix on the Oil Market:
The Economic Consequences of a War with Iraq
William D. Nordhaus, Yale University
October 29, 2002
Models of the oil market are extremely complex. The estimates
prepared by Perry have been compared with a simplified growth model of
the U.S. economy. This appendix explains the model and the basic results.
The model assumes that output is entirely consumption goods. The major
component is a production function in which the only endogenous input is
oil imports. Production is a putty-clay technology in oil inputs and other
exogenous inputs, with Cobb-Douglas substitutability ex ante and fixed
proportions between output and oil imports ex post. The model is a fullemployment model that calculates the terms of trade effects along with the
effects of substitution of other inputs for oil. The investment-output ratio is
assumed to be constant over time.
Five parameters are central to the model’s performance: the initial level
and the growth of total factor productivity, the elasticity and the rate of
change of the elasticity of output with respect to oil imports, and the
depreciation rate of the capital stock. Note that the depreciation rate is central
because it determines the speed with which oil demand responds to changes
in oil prices. It is assumed that capital is never scrapped, which is realistic
when oil imports are a very small share (roughly 2 percent) of costs. The
model’s five parameters are determined by minimizing a loss function that is
a weighted sum of the squared errors of GDP and oil imports over the period
1960-2000. The central estimate is for a depreciation rate of 0.018 percent per
year. One final parameter is the time path of the response of oil prices to
shocks. These results are consistent with recent studies of the oil market.1
Real oil prices are exogenous during the historical period. Based on the
behavior of oil prices in the 1970-2000 period, I estimate that oil regresses
back to the trend at a rate of 20 percent per year after either a good or bad
shock.
See James D. Hamilton, “What is an Oil Shock?” NBER Working Papers 7755, National Bureau of
Economic Research, 2000. The results are similar to the putty-clay model developed in Andrew
Atkeson and Patrick J. Kehoe, “Models of Energy Use: Putty-Clay Versus Clay-Clay,” American
Economic Review, September 1999, pp. 1028-043.
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Using the model, we estimate the impact of both Perry’s “worse” case
as well as the “happy” case of an increase in oil production. Figure 3 shows
the value of oil imports (in 2002 prices) for the estimated model along with
the actual numbers. Figure 4 shows the estimated and actual physical oil-real
GDP ratios. The fit looks misleadingly good because most of the movement is
due to the to oil prices. Figure 5 shows the actual and calculated volume of
oil imports. The model captures the broad trends but cannot resolve the
short-run turning points precisely.
The base case assumes that real oil prices grow at 2 percent per year
after averaging $25 per barrel in 2002. I estimate Perry’s “worse” case by
setting the real oil price at $75 per barrel in 2003 and then allowing the real
price to regress 20 percent per year back to the baseline. The “happy”
outcome is somewhat more complex. It assumes that Iraq builds up its
production by 1 mbpd relative to the baseline; that Saudi Arabia and other
supplier countries reduce their supply by one-third of the increased Iraqi
production; that oil production then regresses back to the baseline at 20
percent per year after 2008; and that world oil demand is four times as large
as U.S. demand and has equal elasticities. The model then solves for the price
trajectory that balances supply and demand.
The important results of the model are shown in Table A-1. The first
column shows the terms of trade impacts – that is, the impacts of the shocks
on the real cost of oil imports. The second column shows the impact on real
net domestic product (which is the appropriate welfare measure of output).
The final column shows real national income, which is real output corrected
for the terms of trade effect. The third column equals the sum of the first two.
The bottom rows show the elasticities of the demand for imported oil with
respect to the crude oil price. These are close to the estimates used by Perry
and found in the literature.
The effects of oil shocks are actually quite subtle. When capital
adjustment is slow, most of the impacts are on the terms of trade in the first
column. When capital adjustment is very fast, most of the impacts are on
output through the requirement of substitution of other inputs for oil. And
the effect is obviously larger if prices regress more slowly back to their
baseline path.
The high-cost case of $500 billion is consistent with a number of
possible combinations of parameters in the oil model. Looking at the last
column of Table A-1, a long lifetime and rapid regression of price to trend
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yields $468 billion. A short lifetime and a slow regression of price to trend
yield $650 billion. Even instantaneous adjustment and slow regression yield a
number near the high-cost figure in Table 7. Note as well that these assume
perfect competition, no economic frictions, and no political sand in the gears
of market reactions.
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Value of
Oil
Imports
Real
National
Real NDP Income (a)
[Billions, discounted costs for first
decade, 2002 prices]
Capital lifetime of 14 years
Price regression
20 % per year
50 % per year
623
291
-346
-177
-968
-468
175
116
-475
-219
-650
-335
2
-588
-590
Capital lifetime of 3 years
Price regression
20 % per year
50 % per year
Instantaneous capital adjustment
20 % per year
Item: Elasticity (b)
1-year
10-year
-0.055
-0.561
(a) Real national income equals NDP corrected for terms of trade effects.
(b) Elasticity of quantity of oil imports with respect to crude oil price.
Table A-1. Cost of Perry’s “Worse” Oil Shocks in Full Employment Model
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Value of Oil Imports
Value of oil imports (billions, 2002 $)
160
140
120
Simul
Actual
100
80
60
40
20
0
1970
1975
1980
1985
1990
1995
2000
Figure 1. Estimated and Actual Value of Oil Imports, 1970-2000 (billions in
constant prices)
Oil import/GDP
Value Oil Imports/GDP (percent)
4%
Simul
Actual
3%
2%
1%
0%
1970
1975
1980
1985
1990
1995
Figure 2. Share of Oil Imports in GDP, 1970-2000
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2000
Oil Imports (billions of barrels per year)
Volume of Oil Imports
5
Simul
Actual
4
3
2
1
0
1970
1975
1980
1985
1990
1995
2000
Figure 3. Actual and Projected Volume of Imports (billions of barrels)
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